December 17, 1908] 



NA TURE 



209 



the late Prof. \V. Cassie. In this method use is made 

 of the periods of small oscillations of a balance-beam. 

 The method consists in taking as standard moment of 

 inertia a known mass hung from the knife-edge of a 

 balance and comparing others with it. The time of swing 

 is taken with the standard mass in one pan and a counter- 

 poise in the other. The body the moment of inertia of 

 which is required is attached to the beam in such a 

 manner that the coefficient of the directive couple is un- 

 altered, and the time of swing is determined without 

 weights in the pans. From these times, with a know- j 

 ledge of the length of the beam and the masses used, the 

 moment of inertia required is easily calculated. — The I 

 diffusion of actinium and thorium emanations : S. Russ. 

 Experintents were described in which the emanation of 1 

 actinium was allowed to diffuse into the following gases : — j 

 air, hydrogen, carbon dioxide, sulphur dioxide, and argon. 

 The diffusion coefficients of the emanation in these gases 

 agree in general with those calculated by means of 

 Graham's law, making use of the diffusion coefficient in 

 air. The variation with pressure of the diffusion coefficient 

 of the actinium emanation in air was shown to be quite 

 in accordance with the ordinary gas laws, down to a few 

 centimetres pressure, the product of the pressure and 

 diffusion coefficient remaining practically constant. Ex- 

 periments under identical experimental conditions with 

 thorium emanation over a similar range of pressure also 

 yield nearly a constant value for the product of pressure 

 and diffusion coefficient. The' ratio of the two constants 

 thus obtained leads directly to a ratio of the molecular 

 weights of the two emanations, the result being that 

 thorium emanation appears to have about 1-4 times the 

 molecular weight of actinium emanation. — The elliptic 

 polarisation produced by the direct transmission of a plane 

 polarised stream through a plate of quartz, cut in the 

 direction oblique to the optic axis, with a method of deter- 

 mining the error of a plate supposed to be perpendicular 

 to the axis : J. Walker. — \n experimental investigation 

 of Gibbs's theory of surface-concentration regarded as the 

 basis of adsorption : W. C. M. Lewis. 



Geological Society, December 2. — Prof. W. J. Sollas, 

 K.R.S., president, in the chair. — The geological inter- 

 pretation of the earth-movements associated with the 

 Californian earthquake of .April 18, 1906 : R. D. Oldham. 

 At the time of the San Francisco earthquake movement 

 took place along a fault, known as the San .'\ndreas 

 fault, which can be traced for a distance of about 200 

 miles. \ re-measurement of the primary triangulation in 

 the region shaken by the earthquake revealed consider- 

 able displacements, increasing in amount as the fault is 

 neared, and of such nature that places to the east of 

 the fault were shifted southwards, while those to the 

 west of it were shifted northwards. The extent and 

 peculiar distribution of these displacements negative the 

 supposition that the fault was the cause — it must rather 

 be regarded as a consequence of, or an incident in, the 

 earthquake, this word being used to denote the disturb- 

 ance in its entirety. The author considers that the dis- 

 placements cannot be explained in a satisfacfory manner 

 on the supposition that they are the result of strains affect- 

 ing the crust of the earth as a whole, but may be ex- 

 plained by the difference in character and behaviour of the 

 materials composing the greater part of it, where pressures 

 are great enough to produce the phenomena of solid flow, 

 and of those in the outer skin, where the pressures are 

 not great enough to produce any material difference in the 

 behaviour of rocks from that which we associate with 

 solidity, as experienced at the surface of the earth. The 

 surface-displacements constituting the earthquake, as 

 ordinarily understood, arise from disturbances in the outer 

 skin ; but in great earthquakes, like the one dealt with 

 in the paper, these may be the result of more deep-seated 

 disturbances affecting the whole crust of the earth. 



Linnean Societv. Decerriher 3. — Dr. D. H. Scolt, 

 l'".R.S.. president, in the chair. — Biscayan plankton : a 

 memoir on the Ostracoda captured during the 1900 cruise 

 of H.M.S. Research : Dr. G. Herbert Fowler. More 

 than 7000 specimens had been identified, and in the case 

 of more than 3000 the sex had been determined and the 

 lengths of the shells measured. ,-\s the resul: n! these 



measurements, the writer was enabled to formulate pro- 

 visionally a new law of growth in Crustacea : — " During 

 early growth each stage increases at each moult by a 

 percentage of its length, which is constant for the species 

 and sex." For this the name of Brooks's law was sug- 

 gested. Prof. W. K. Brooks having made the first 

 observations which led to it ; it had been checked to some 

 extent by observations on lobsters (Herrick) and crabs 

 (Waddington). — Mimicry in spiders : R. Innes Pocock. — 

 Note on Juiiipenis taxifolia, Hook, and Arn. : Bunzo 

 Hayata. This species had been described from specimens 

 from the Bonin Islands, but had also been recorded from 

 the province of Hupeh, China ; further examination shows 

 that the Chinese plant is specifically distinct from that 

 occurring in the Bonin Islands. 



Mathematical Society, Dccmiber 10.— Sir W. D. Niven, 

 president, in the chair. — The theory of waves propagated 

 vertically in the atmosphere : Prof. H. Lamb. Two cases 

 are considered. In one the undisturbed atmosphere is taken 

 to be at a uniform temperature. In the second the tempera- 

 ture gradient is taken to be uniform, the temperature 

 diminishing upwards. In both, the variations of pressure 

 and density involved in the propagation of the waves are 

 taken to follow the adiabatic law. Even when viscosity is 

 taken into account, it appears that the amplitude of the 

 waves, due to arbitrary initial disturbances, tends to increase 

 indefinitely as the waves travel upwards. One unexpected 

 result is ' that an unlimited atmosphere may possess a 

 definite natural period of vibration in the sense that an 

 impressed local periodic force, of this, but of no other, 

 period, would generate an oscillation of continuously in- 

 creasing amplitude.— The representation of a function by 

 series of Bessel's functions : Dr. E. W. Hobson. The 

 question considered is that of the convergence of a series 

 of the kind that arises in the problem of the vibrations of 

 a membrane or the two-dimensional vibrations of gas in 

 a circular cylinder. It is shown that the series converges 

 and its sum represents the function which it is meant to 

 represent, in the same way as Fourier's series represents 

 a function, provided that the function is integrable accord- 

 ing to Lebesgue's extended definition, and that if the func- 

 tion is infinite at the origin, the infinity is not of too 

 high an order. The order in question must be less than 

 — Theorv of Cauchy's principal values (fourth paper) : 

 G. H. -Hardy. The paper deals with the possibility of 

 interchanging the order of integrations in repeated infinite 

 integrals which have finite princip.al values. A number of 

 results bearing on the problem of the inversion of a definite 

 integral are obtained.— Differentials : Dr. W. H. Young. 

 It is shown that in the case of any number of variables 

 the differentials take precisely the place in expansion 

 theorems which are occupied by the successive differential 

 coefficients in the case of functions of one variable.— The 

 solution of the homogeneous linear difference equation of 

 the second order: G. N. Watson. The problem is thatof 

 determining a function of the complex variable x which 

 satisfies the equation 



Aix)f{x+i) - B(x)f{x) + C(x)f(x - I) = 0, 

 wherein A{x), B(x), C(.v) are known uniform functions. 

 It is shown that the required function can be determined 

 provided the functions A, B, C satisfy restrictive con- 

 ditions which are satisfied by wide classes of functions.— 

 Four svstems of three quaternary quadrics that can be 

 expressed bv means of five squares : Prof. A. C. Dixon. 



(i) The reduction of a quaternary cubic from the sum of 



six cubes to the sum of five ; (2) addition to a paper on 

 the eliminant of three quantics in two independent vari- 

 ables : \. L. Di«on.— Note on a continued fraction equi- 

 valent to the remainder after n terms of Taylor's series : 

 Prof. L. J. Rogers. — Solid angles and potentials of plane 

 discs : Balak Ram.— A method of -solving the problem of 

 Mersrnnc's numbers : Dr. T. Stuart. 



EDINIiURGH. 



Royal Society. November 16.— Dr. Burgess, vice-presi- 

 dent in the chair. — .'\n investigation of the seiches of 

 Locli Earn bv the Scottish Lake Survey, parts iii.-v. : 

 Prof. Chrystal. The part of this memoir communicated 

 bore specially upon the endeavour, by critical examina- 

 tion of seiche records, chiefly on Loch Earn, to come to 

 ' some definite conclusion as to the origin of the seiche. 



NO. 2042, VOL. 7q] 



